# Offer curves in general equilibrium

I'm having trouble understanding how to find the offer curves in general equilibrium. Is there a general way that we can use to find it?

I can understand the Pareto set and contract curve but when it comes to equilibrium I'm stuck.

For ex. if we have two consumers: Consumer 1 has as his initial bundle all of good $$2:(0; 10)$$ ; while consumer 2 has all of good $$1 : (10; 0)$$.

Let their utilities be $$u_1= min (x; y)$$ $$u_2= min (4x; 5y)$$

What would be the steps for finding the offer curves? Appreciate any help given.

In the picture below offer curve of individual 1 is given by lines connecting $$E$$ to $$O_1$$ and $$O_1$$ to $$O_2$$. And offer curve of individual 2 is given by lines connecting $$E$$ to $$O_2$$ and $$O_2$$ to $$A$$ and $$A$$ to $$O_1$$. Set of competitive equilibria are given by the intersection of two offer curves. $$p_X = 0$$ and $$p_Y = 1$$ supports allocation at $$O_2$$ as competitive equilibrium. Allocations on the line segment $$O_1A$$ are supported by prices $$p_X = 1$$ and $$p_Y = 0$$. 